I have seen no specific study done on this subject, but with a little bit of scribbling on a napkin, I would think that only 3-5% of players are ahead after a long period of time.
Consider tournaments for a moment. It is known that only 10-15% of the players in any given tournament will get any money back at all. This does not yet make them long term winners. Then consider how often a player will cash. Very good players may cash more than 20% of the time. It is said that some pro tournament players cash 15-18% or the time, but these are likely very deep runs.
Tournaments are good to use for this assessment, because money is guaranteed to someone. In a cash game, there are no guaranteed winners - because of rake, it is possible that 10 players can move money around the table all night long and the only one that actually makes any money is the casino (unlikely but possible).
If we assume a group of players will play 100 x 100 player tournament with $100 buyin with 20% in fees with 15% player payout:
A player cashing 5% of the time cannot breakeven, even if they finish in first place those 5 times. A player cashing 10% of the time must finish in 3rd place all 10 times (or equivalent winnings) in order to breakeven. A player cashing 15% of the time must finish in 4th place (or equivalent winnings) all 15 times in order to breakeven.
The point of this is to illustrate just how difficult it is to be a winning player at poker. It is completely reasonable to assume that only 3-5% of the players are winners over the long term.